Quickest Change Detection of Unknown Mean-Shifts using the James-Stein Estimator

Abstract

This paper addresses the problem of quickest change detection of an unknown mean-shift in multiple Gaussian data streams. We propose a novel extension of the window-limited CuSum (WL-CuSum) test which utilizes the James-Stein estimator to improve detection performance. Compared to traditional maximum likelihood-based approaches, the proposed approach can considerably reduce the detection delay, especially when the number of streams is large. Our theoretical results indicate that the proposed test asymptotically optimal, and non-asymptotically a uniform improvement over its maximum likelihood alternative. The performance is improved for all values of the unknown post-change parameter, as long as the number of the data streams is greater than three. Overall, the results suggest that shrinkage estimators, such as the James-Stein estimator, can provide substantial performance improvement in change detection problems with unknown parameters.